The forward-backward splitting algorithm for monotone inclusion problems was first introduced by Lions and Mercier [1]}. In the work of Lions and Mercier, other splitting methods, such as Peaceman–
Rachford algorithm [2]} and Douglas-Rachford algorithm [3]} was developed to find the zeros of the sum of two maximal monotone operators.
Since then, it has been studied and reported extensively in the literature; see, for instance, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} and the references therein.
Recently, stochastic versions
of splitting algorithms for monotone inclusions have been proposed, for example stochastic forward-backward splitting method [11]}, [12]},
stochastic Douglas-Rachford splitting method [13]}, stochastic reflected forward-backward splitting method [14]} and stochastic primal-dual method [15]}, see also [16]}, [17]}, [18]} and applications to stochastic optimization [11]}, [20]} and
machine learning [21]}, [22]}.
